If you're awake, and the area of a Silence spell overlaps you I'm pretty sure there's no way you can miss it - even if there's noone talking around you, there's still a whole bunch of environmental sounds that suddenly disappear.
Taking example from where I'm sitting right now at my computer desk - if a silence spell were dropped in this room, I wouldn't be able to hear my breath thru my nose, the soft hum of the computer fan, the gentle breeze outside rustling the grass and trees slightly, birds chirping far far off in the distance, some guy mowing his lawn the next block or so over, etc. It would immediatly click that something isn't right - even if you have earplugs in you can hear something. Even if it were at night where none of the normal days activities were taking place, you'd still have the sounds of your own body just go away - sound your clothes make when you shift your weight, the rubbing sound when you get a peice of grit out of your eye, and whatnot.
If you're awake, I'd put the listen check to notice a silence spell that is affecting you at DC 0.
If your in the open, and there's a silence area somewhere that's kinda nearby but doesn't include the area you're in I'd put the listen DC at something like 20, maybe 25 or higher. Unless it's something real obvious -the creaking of a mill just stops totally dead, for instance- it would be a pain to notice a hole in environmental sound. If the silence area is affecting something significant (mill, example) I'd put the DC at 12 plus distance modifier (+1/10ft away).
If you're asleep, well.. you're asleep - you shouldn't be able to notice a silence spell that doesn't directly overlap you at all. If the silence goes over you yourself while asleep that's a bit different - certain very subtile cues that you're accustomed to while sleeping arn't there for some reason, which could have your body telling you "Hey! Wake up, something's not right!", but not necessarily. Some folks would wake up if the sound of their computer fan went dead, me personally I'd be out like a light - it normally takes something about as loud as music being played on the radio in the next room, or the garbage truck taking the trash, or the shower being run to wake me up. Heh, lack of sound would probably make me sleep more soundly. At a guess, I'd put the listen DC for noticing silence while asleep at 19 + 1d6 (to represent some people sleeping more soundly then others), possibly maybe even as high as 24 + 1d6.